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Neural Networks For Constrained Optimization Problems, Walter E. Lillo, Stefen Hui, Stanislaw H. Zak
Neural Networks For Constrained Optimization Problems, Walter E. Lillo, Stefen Hui, Stanislaw H. Zak
Department of Electrical and Computer Engineering Technical Reports
This paper is concerned with utilizing neural networks and analog circuits to solve constrained optimization problems. A novel neural network architecture is proposed for solving a class of nonlinear programming problems. The proposed neural network, or more precisely a physically realizable approximation, is then used to solve minimum norm problems subject to linear constraints. Minimum norm problems have many applications in various areas, but we focus on their applications to the control of discrete dynamic processes. The applicability of the proposed neural network is demonstrated on numerical examples.
Neural Networks For Constrained Optimization Problems, Walter E. Lillo, Stefen Hui, Stanislaw H. Zak
Neural Networks For Constrained Optimization Problems, Walter E. Lillo, Stefen Hui, Stanislaw H. Zak
Department of Electrical and Computer Engineering Technical Reports
This paper is concerned with utilizing neural networks and analog circuits to solve constrained optimization problems. A novel neural network architecture is proposed for solving a class of nonlinear programming problems. The proposed neural network, or more precisely a physically realizable approximation, is then used to solve minimum norm problems subject to linear constraints. Minimum norm problems have many applications in various areas, but we focus on their applications to the control of discrete dynamic processes. The applicability of the proposed neural network is demonstrated on numerical examples
Minimizing Quotient Space Norms Using Penalty Functions, Stefen Hui, Walter E. Lillo, Stanislaw H. Zak
Minimizing Quotient Space Norms Using Penalty Functions, Stefen Hui, Walter E. Lillo, Stanislaw H. Zak
Department of Electrical and Computer Engineering Technical Reports
A penalty function method approach is proposed to solve the general problem of quotient space norms minimization. A new class of penalty functions is introduced which allows one to transform constrained optimization problems of quotient space norms minimization by unconstrained optimization problems. The sharp bound on the weight parameter is given for which constrained and unconstrained problems are equivalent. Also a computationally efficient bound on the weight parameter is given. Numerical examples and computer simulations illustrate the results obtained.